Question

Это интеграл
{xdx/(x^2+1)^2=

Answer 1

$\int \frac{xdx}{( {x}^{2} + 1)^{2} } = \int \frac{x}{ {t}^{2} } \times \frac{1}{2x} dt = \\ {x}^{2} + 1 = t, \: dt = 2xdx, \: dx = \frac{1}{2x} dt \\ = \frac{1}{2} \int {t}^{ - 2} dt = - \frac{1}{2t} = - \frac{1}{2( {x}^{2} + 1) } + C$